If you want to buy your own set of cues, nowadays there are several online pool cues store to supply you wide variety of cues and other billiard accessories, but more importantly, there are local stores that specialize in ensuring you get just the right cue to fit your playing style. The key to unlocking the hidden structure of a chaotic system is in determining its preferred set of behaviours - known to mathematicians as its attractor. Mathematicians use the concept of a "phase space" to describe the possible behaviours of a system geometrically. Chaos Theory is not solely the providence of mathematicians. It was the first chaotic system to be discovered, long before there was a Chaos Theory. In 1887, the French mathematician Henri Poincaré showed that while Newton’s theory of gravity could perfectly predict how two planetary bodies would orbit under their mutual attraction, adding a third body to the mix rendered the equations unsolvable.

The branch of fractal mathematics, pioneered by the French American mathematician Benoît Mandelbröt, allows us to come to grips with the preferred behaviour of this system, even as the incredibly intricate shape of the attractor prevents us from predicting exactly how the system will evolve once it reaches it. The mathematician Ian Stewart used the following example to illustrate an attractor. Though we may not be able to predict exactly how a chaotic system will behave moment to moment, knowing the attractor allows us to narrow down the possibilities. It also allows us to accurately predict how the system will respond if it is jolted off its attractor. No matter where it starts, the ball will immediately move in a very predictable way towards its attractor - the ocean surface. A chaotic system will also move predictably towards its attractor in phase space - but instead of points or simple loops, we see "strange attractors" appear - complex and beautiful shapes (known as fractals) that twist and turn, intricately detailed at all possible scales. Once there it clings to its attractor as it is buffeted to and fro in a literal sea of chaos, and quickly moves back to the surface if temporarily thrown above or dumped below the waves.

The behaviour of the system can be observed by placing a point at the location representing the starting configuration and watching how that point moves through the phase space. You can visualise it like this: put a loop of string around pins located at the foci, then pull the string taut at one point using a pencil. Notice that three points are aligned: the point marking your position, the point on the mirror where you see the reflection of the object and the (imaginary) point behind the mirror where you believe the object to be. To prove our claims above, we are going to exploit this simple idea, the mirror being one side of the billiard table. In phase space, a stable system will move predictably towards a very simple attractor (which will look like a single point in the phase space if the system settles down, or a simple loop if the system cycles between different configurations repeatedly). The purpose of a defibrillator - the device that applies a large voltage of electricity across the heart - is not to "restart" the heart cells as such, but rather to give the chaotic system enough of a kick to move it off the fibrillating attractor and back to the healthy heartbeat attractor.

Fortunately, this intricate state of synchronisation is an attractor of the system - but it is not the only one. If the system is jolted somehow, it may find itself on an altogether different attractor called fibrillation, in which the cells constantly contract and relax in the wrong sequence. The main benefit to having a chaotic heart is that tiny variations in the way those millions of cells contract serves to distribute the load more evenly, reducing wear and tear on your heart and allowing it to pump decades longer than would otherwise be possible. These millions of cells must work in sync, contracting in just the right sequence at just the right time to produce a healthy heartbeat. The millions of cells that make up your heart are constantly contracting and relaxing separately as part of an intricate chaotic system with complicated attractors. The facilities provided are no less than a five star hotel. An active retirement life is what today's senior citizens want and for that it is essential to look for the best retirement communities which offer access to various facilities like swimming pools, boating, club houses, art and craft and golf courses. According to Paul Brown, Red Baron's Publisher and antiques guru, the trick to finding antiques is a combination of participating in the word-of-mouth antiques network and "beating the bush." Red Baron rarely has difficulty locating and obtaining pieces; they have antiques and art experts stationed in different regions all over the world scouring estate sales and other antique markets for pieces to ship back to Atlanta.

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